Concept explainers
In Exercises 15–20, decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game. [HinT: See Example 4.]
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Finite Mathematics
- In Section 5.5 we showed the following two-person, zero-sum game had a mixed strategy: Player B b1 b2 b3 a1 0 -1 2 Player A a2 5 4 -3 a3 2 3 -4 a. Which strategies are dominated? a1, a2, a3, b1, b2, b3 b. Does the game have a pure or mixed strategy?arrow_forwardIn game theory, the strategy that has a higher payoff than any other strategy—no matter what theother player does—is also known as the:a) superior strategy.b) Nash equilibrium.c) dominant strategy.d) best possible outcome..arrow_forwardconsider the ff game in the normal form: which of the ff is true: a. the game has dominant equilibrium A3, B3 b. A3 always dominates A2 c. A3 is a dominant strategy for Player A d. B3 is a dominant strategy for Player Barrow_forward
- Decide whether the game is strictly determined. If it is, give the players' optimal pure strategies and the value of the game. a. A's optimal strategy is b; B's optimal strategy is p; value: 1 b. The game is not strictly determined c. A's optimal strategy is b; B's optimal strategy is q; value: 0.5 d. A's optimal strategy is a; B's optimal strategy is p; value: 2 e. A's optimal strategy is a; B's optimal strategy is q; value: 1arrow_forwarda.Discuss five assumptions of game theory b.Explain three steps required to find a saddle pointarrow_forwardA game theorist is walking down the street in his neighborhood and finds $20. Just as he picks it up, two neighborhood kids, Jane and Tim, run up to him, asking if they can have it. Because game theorists are generous by nature, he says he’s willing to let them have the $20, but only according to the following procedure: Jane and Tim are each to submit a written request as to their share of the $20. Let t denote the amount that Tim requests for himself and j be the amount that Jane requests for herself. Tim and Jane must choose j and t from the interval [0,20]. If j + t ≤ 20, then the two receive what they requested, and the remainder, 20 - j - t, is split equally between them. If, however, j + t > 20, then they get nothing, and the game theorist keeps the $20. Tim and Jane are the players in this game. Assume that each of them has a payoff equal to the amount of money that he or she receives. Find all Nash equilibria.arrow_forward
- Consider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.arrow_forwardQ1. Explain the concept of two-person zero- sum game strategy and saddle point. Also provide a suitable example. A. In a certain game player has three possible courses of action L, M and N, while B has two possible choices P and Q. Payments to be made according to the choice made. Choices Payments L,P A pays B OMR 4 L,Q B pays A OMR 4 M,P A pays B OMR 3 M,Q B pays A OMR 4 N,P B pays A OMR 3 N,Q B pays A OMR 4 What are the best strategies for players A and B in this game? What is the value of the game for A and B? For what value of q, the game with the following payoff matrix is strictly determinable? Player A Player B B1 B2 B3 A1 Q 7 3 A2 -1 Q -6 A3 -3 5 Qarrow_forward